Position 54, page 86
From Backgammon, the Cruelest Game, by Barclay Cooke and Jon Bradshaw

Black to play 6-1.

After 21/15, black has a 1 to play is trying to save (avoid losing) a double game. Sometimes the playing of a simple 1 is essential to one’s basic strategy, though many players seem to feel that because the roll moves so short a distance and wields no apparent power, it is unimportant. Nothing could be further from the truth. The example shown in Diagram 54 is indicative of this.

By playing the 1 correctly here, black increases his chances of saving the double game by exactly 100 percent. It is a good example of how subtle the playing of 1’s can be and how careless play can penalize the unobservant player. Many players, nearly resigned to losing the double game and believing the movement of the 1 to be relatively unimportant, would move it from white’s 10 point to the 11 point in order to move that much close home. But by so doing, they have limited themselves to only two rolls that could save them: double 4’s and double 6’s, a 17 to 1 shot.

Had they left the outside man where it was, however, and moved a 1 from black’s 4 point to the 3 point, double 5’s and double 3’s would also have saved the double game. Black would now be only an 8 to 1 underdog — assuming, of course, that white did not throw a double himself.

Not: 21/14 21/15, 4/3
Rollout

Tom Keith 2013
Money play
Black owns 2-cube
Black rolls 6-1

1296 games with VR
Checker play: 3-ply
Cube play: XG Roller
XGID=-BB-E-E--------------A--c-:1:1:1:61:0:0:0:0

 6-1: Game G BG Equity 1 21/15, 4/3 W L .0000 1.000 .0000 .9074 .0000 .0000 −1.9074 2 21/15, 6/5 W L .0000 1.000 .0000 .9306 .0000 .0000 −1.9306 (0.0232) 3 21/15, 2/1 W L .0000 1.000 .0000 .9306 .0000 .0000 −1.9306 (0.0232) 4 21/14 W L .0000 1.000 .0000 .9537 .0000 .0000 −1.9537 (0.0463) Not

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List of Positions from Backgammon, the Cruelest Game

Backgammon, the Cruelest Game (1974), by Barclay Cooke and Jon Bradshaw